Method of estimating the properties of a polymer product

ABSTRACT

The present invention relates to a method of estimating the properties of a polymer product by using converted process variables (cPV&#39;s) which means process variable that final or intermediate product experienced earlier in average in the reactors by stage with respect to the final product, which incorporates residence time distribution to process variables, wherein said method comprises the following steps of: computing cPV&#39;s by incorporating the residence time distribution to said process variables by means of theoretically determining the amounts of content and discharge of the product in the process, and then solving the balance equations of a hypothetical substance by taking the respective process variables as those of the hypothetical substance: and estimating the properties of the product by inputting to various property estimation models cPV&#39;s in the reactors by stage with respect to the final product after incorporating the residence time distribution to said process variables.

TECHNICAL FIELD

[0001] The present invention relates to a method of estimating theproperties of a polymer product, or more particularly to a method ofestimating the properties of a product by using converted processvariables (cPV's) which means process variable that final orintermediate product experienced earlier in average in the reactors bystage with respect to the final product, which incorporates residencetime distribution to process variables, wherein said method comprisesthe following steps of: incorporating the residence time distribution tosaid process variables by means of theoretically determining the amountsof content and discharge of the product in the process, and then solvingthe balance equations of a hypothetical substance by taking therespective process variables as those of the hypothetical substance; andestimating the properties of the product by inputting to variousproperty estimation models cPV's in the reactors by stage with respectto the final product after incorporating the residence time distributionto said process variables.

BACKGROUND ART

[0002] Generally, the adjustment of physical properties of polyolefin ina commercial plant is largely dependent on experiences of a skilledoperator. However, because of the differences in modes of operations ofrespective operators, the operations are sometimes inconsistent. Themodes of operations which are different from operator to operator affectthe physical properties of a product (i.e., uniformity) and in the end,even if the products are of the same grade, there still may bedifferences depending on the lots. Obviously, this is a potential causeof claims or complaints from the end users.

[0003] In order to overcome these problems, it is useful to apply thetechnology, which allows estimation of properties of a product, at thepoint of its production.

[0004] Conventionally, in estimating the properties of a polymerproduct, various empirical and statistical models have been mainly used,such as empirical correlation, neural network, or partial least square(PLS) models.

[0005] While the correlation models of prior art can be relativelyeasily applied to the steady states wherein the process conditions arestably maintained, the conventional technology is problematic in that itfrequently shows large differences from the actual analysis values inthe unsteady states or in a grade change, where the process conditionsare in the state of flux.

[0006] These differences are due to the existence of a process delay.The process delays are expressed in different forms, depending on theintrinsic residence time distribution of various devices. For example,there is a simple case of a push back to a certain period of time (e.g.,in pipes), or there may be a push back of extended effects in the forman exponential function, such as in continuous stirred tank reactors(CSTR). For other reaction devices, there may be other peculiar types ofresidence time distribution.

[0007] In particular, in cases of multi-stage continuous polymer plants,up until to the point that the product would be affected by the extendedeffects caused by a change in operational conditions of the previousstage, there would be a long time delay, depending on the intrinsicresidence time distribution characteristics of the process.Consequently, because of a rather simplistic way of estimating theproperties of a polymer product from the process variables of thecurrent states, it would be of course accompanied by a significantdegree of error.

[0008] Meanwhile, a typical method of estimating the properties ofpolymers by incorporating the residence time distribution of the processis by means of a physical model. It is a method of establishing balanceequations for a substance by way of reaction system and then solvingsaid equations. For this method based on said physical model, it isnecessary to obtain reaction rate constants and various types ofphysiochemical constants. However, there lies the problem since it isnot so easy to obtain these types of constants. To solve this problem ofphysical model, the method widely used in the industry is a method ofcomputing cumulative properties (hereinafter cumulative propertiesmodel) by calculating the instantaneous properties of a product,followed by the application of residence time distribution and themixing rule of polymer properties.

[0009] The method according to said cumulative properties model has manyadvantages, such as easy application to the actual process in somecases, and potential utilization of empirical correlation, neuralnetwork, PLS models, etc. in estimation of instantaneous properties.However, with respect to the method of cumulative properties model,there is a problem of requiring “model training,” or the data of thesteady states for the purposes of carrying out the process of empiricalcorrelation, neural network, or PLS for estimating the properties of aproduct. In particular, in case of a system with recycle streams whichare not maintained constantly by time, it is almost impossible to applythe cumulative properties model.

DISCLOSURE OF THE INVENTION

[0010] In order to solve the problems of prior art as above, the presentinvention seeks to provide a method of applying cPV's in operation inthe reactors by stage, such as temperature and pressure, to the modelsof estimating the properties of a product by processing the processvariables by incorporating the residence time distribution to theprocess variables themselves by way of further simplification of thecumulative properties model which finds cumulative properties by meansof residence time distribution and the nixing rule of polymer propertiesby computing the instantaneous properties from the current values ofprocess variables.

[0011] The present invention relates to a method of estimating theproperties of a product by using cPV's in the reactors by stage withrespect to the final product, which incorporates residence timedistribution to process variables, wherein said method comprises thefollowing steps of: computing cPV's in the reactors by stage withrespect to the final product by incorporating the residence timedistribution to said process variables by means of theoreticallydetermining the amounts of content and discharge of the product in theprocess, and then solving the balance equations of a hypotheticalsubstance by taking the respective process variables as those of thehypothetical substance; and estimating the properties of the product byinputting to various property estimation models cPV's in the reactors bystage with respect to the final product after incorporating theresidence time distribution to said process variables.

[0012] Moreover, in relation to the method of monitoring the state ofprocess incorporating the residence time distribution to the processvariables, the present invention relates to a method of monitoring thestate of process, wherein said method comprises theoreticallydetermining the amounts of content and discharge of the product in theprocess, and then incorporating the residence time distribution to saidprocess variables by way of the method of solving the balance equationsof a hypothetical substance by taking the process variables as those ofthe hypothetical substance; and monitoring the state of process byinputting to various process-state-monitoring models cPV's in thereactors by stage with respect to the final product after incorporatingthe residence time distribution to said process variables.

BRIEF DESCRIPTION OF DRAWINGS

[0013]FIG. 1 is a bloc diagram, which illustrates the method ofestimating the properties of a polymer product according to the presentinvention.

[0014]FIG. 2 is a graph, which conceptually explains the need forincorporating residence time distribution to various process variablesaccording to the present invention, with an example of a continuousstirred tank reactor (CSTR).

[0015]FIG. 3 is a graph, which shows the raw data of reactortemperatures and pressures as a function of time. The reactortemperature is one of the important elements in operating the reactionprocess of high-density polyethylene (HDPE).

[0016]FIG. 4 is a graph, which shows the raw data of mass flow rates ofethylene and hexane into the inner chamber of a reactor as a function oftime. The rate is one of the important elements in operating thereaction process of high-density polyethylene (HDPE).

[0017]FIG. 5 is a graph, which shows the raw data of mole ratios ofhydrogen and ethylene (H2/C2) and cPV's as a function of time. The moleratio is one of the important elements in operating the reaction processof high-density polyethylene (HDPE).

[0018]FIG. 6 is a graph, which shows the estimated values of melt indexof an intermediate product as a function of time from the outlet of afirst-stage reactor in the reaction process of HDPE according to thepresent invention.

[0019]FIG. 7 is a graph, which shows the estimated values of melt indexof the final product as a function of time from the outlet of asecond-stage reactor in the reaction process of HDPE according to thepresent invention

BEST MODE FOR CARRYING OUT THE INVENTION

[0020] The present invention is described in further detail with anexample as below: Nevertheless, it is described here for illustrativepurposes only and does not limit the present invention in any manner.

[0021]FIG. 1 is a bloc diagram, which shows the method of estimating theproperties of a polymer product according to the present invention. FIG.1 shows the process of computing cPV's in the reactors by stage withrespect to the final product discharged at a certain time period with agiven operational condition of each stage. This computation was madewith due consideration of residence time distribution.

[0022] The process of computation shown in FIG. 1 is described as below,which computes, with due consideration of residence time distribution,cPV's in the reactors by stage with respect to the final productdischarged at a certain time period.

[0023] First, the raw data such as reactor temperature, pressure, andconcentration were read through a controller, etc. From the raw dataread in as such, the balance equations (Mathematical Formulas 1˜2 asbelow) of a substance with respect to the polymers were constructed.From these balance equations of the substance, M_(ij) could be obtained,which is the mass (kg) of the polymers, polymerized in the i^(th)reactor and passed over thereto, out of the polymers in the j^(th)reactor. Next, W_(f,ij) was obtained, which is the mass flow rate(kg/hr) of the polymers, polymerized in the i^(th) reactor, out of thepolymers fluxed in into the j^(th) reactor. Then, W_(o,ij) was obtained;which is the mass flow rate (kg/hr) of the polymers, polymerized in thei^(th) reactor, out of the polymers discharged from the j^(th) reactor.The mathematical formulas used herein are as follows:

dM _(ij) /dt=W _(f,ij) −W _(o,ij)(i≠j)  Mathematical Formula 1

dM _(ii) =W _(i) −W _(o,ii)(i=j)  Mathematical Formula 2

W_(f,ij)=W_(o,ij−l)  Mathematical Formula 3

W _(o,ij) =wf _(ij) W _(o,j)  Mathematical Formula 4

wf _(ij) =M _(ij) /M _(j)(i≦j)  Mathematical Formula 5

W _(f,12) =W _(f,2) =W _(o,11) =W _(0,1)  Mathematical Formula 6$\underset{\_}{{Mathematical}\quad {Formula}\quad 7}$${{\sum\limits_{i = 1}^{j}{wf}_{ij}} = 1};{{\sum\limits_{i = 1}^{j}M_{ij}} = M_{j}}$

[0024] In the above mathematical formulas, the following conventions areused:

[0025] M_(i): Mass (kg) of polymers in the i^(th) reactor;

[0026] W_(f,i): Mass flow rate (kg/hr) of polymers of inflow to thei^(th) reactor;

[0027] W_(o,i): Mass flow rate (kg/hr) of polymers discharged from thei^(th) reactor;

[0028] w_(f,ij): Ratio (kg/kg) of the amounts of polymers, polymerizedin the i^(th) reactor, out of the polymers in the j^(th) reactor;

[0029] M_(ij): Mass (kg) of polymers, polymerized in the i^(th) reactorand passed over thereto, out of the polymers in the j^(th) reactor;

[0030] t: Time (hr);

[0031] W_(i): Polymerization rate (kg/hr) within the i^(th) reactor;

[0032] W_(f,ij): Mass flow rate (kg/hr) of polymers, polymerized in thei^(th) reactor, out of the polymers fluxed in to the j^(th) reactor; and

[0033] W_(o,ij): Mass flow rate (kg/hr) of polymers, polymerized in thei^(th) reactor, out of the polymers discharged from the j^(th) reactor.

[0034] The above formulas are rearranged as follows:

dM _(ij) /dt=M _(i,j−l)/θ_(j−l) −M _(ij)/θ_(j)(i≠j)  MathematicalFormula 8

dM _(ij) /dt =W _(i) −M _(ii)/θ_(i)(i=j)  Mathematical Formula 9

[0035] In the above mathematical formulas, the following conventions areused:

[0036] θ_(i): Average residence time (hr) in the i^(th) reactor;

[0037] M_(ij): Mass (kg) of polymers, polymerized in the i^(th) reactorand passed over thereto, out of the polymers in the j^(th) reactor; and

[0038] W_(i): Polymerization rate (kg/hr) within the i^(th) reactor.

[0039] Various cPV's were computed by applying the numerical values asobtained above to the balance equations of the hypothetical substance(taking the process variables as those of the hypothetical substance) ofvarious process variables expressed as differential equations. To obtainthe properties of a product, various cPV's as computed above wereinputted to the empirical correlation, neural network, partial leastsquare models, etc. The process as such was repeated for each unit time.

[0040] Moreover, if necessary, the lot average value, lot maximum value,and lot minimum value could be obtained by using the numerical values ascomputed by using cPV's.

[0041] The present invention is now described in further detail withexamples with reactor temperature, which is a typical operationalcondition therein.

[0042] By taking the reactor temperature as that of the hypotheticalsubstance, the balance equations of the hypothetical substance asfollows could be established:

dM _(ij) T _(ij) /dt=W _(f,ij) T _(i,j−l) −W _(o,ij) T_(ij)(i≠j)  Mathematical Formula 10

dM _(ii) T _(ii) /dt=W _(i) T _(i) −W _(o,ii) T _(ii)(i=j)  MathematicalFormula 11

[0043] In the above mathematical formulas, the following conventions areused:

[0044] M_(ij): Mass (kg) of polymers, polymerized in the i^(th) reactorand passed over thereto, out of the polymers in the j^(th) reactor;

[0045] T_(i): Temperature (° C.) in the i^(th) reactor;

[0046] T_(ij): Of the polymers in the j^(th) reactor (or discharged),the average temperature (° C.) in the i^(th) reactor, experienced by theportion produced in the i^(th) reactor;

[0047] t: Time (hr);

[0048] W_(i): Polymerization rate (kg/hr) within the i^(th) reactor;

[0049] W_(f,ij): Mass flow rate (kg/hr) of polymers, polymerized in thei^(th) reactor, out of the polymers fluxed in to the j^(th) reactor; and

[0050] W_(o,ij): Mass flow rate (kg/hr) of polymers, polymerized in thei^(th) reactor, out of the polymers discharged from the j^(th) reactor.

[0051] Of the polymers in the j^(th) reactor (or discharged), ifT_(cum,ij) were taken to be the temperatures experienced in the i^(th)reactor by all of the polymers produced from the first reactor to thei^(th) reactor, the formulas must be changed as follows:$\underset{\_}{{Mathematical}\quad {Formula}\quad 12}$${d{\sum\limits_{k = 1}^{i}{M_{kj}{T_{{cum},{ij}}/{dt}}}}} = {{\sum\limits_{k = 1}^{i}{W_{f,{kj}}T_{{cum},i,{j - 1}}}} - {\sum\limits_{k = 1}^{i}{W_{o,{kj}}{T_{{cum},{ij}}\left( {i \neq j} \right)}}}}$$\underset{\_}{{Mathematical}\quad {Formula}\quad 13}$${d{\sum\limits_{k = 1}^{i}{M_{ki}{T_{{cum},{ii}}/{dt}}}}} = {{{dM}_{i}{T_{{cum},{ii}}/{dt}}} = {{W_{j,i}T_{{cum},{i - 1},{i - 1}}} + {W_{i}T_{i}} - {W_{o,i}T_{{cum},{ii}}}}}$

[0052] In the above mathematical formulas, the followings conventionsare used:

[0053] T_(cum,ij):Of the polymers in the jth reactor (or discharged),the temperatures (° C.) experienced in the i^(th) reactor by all of thepolymers produced from the first reactor to the i^(th) reactor;

[0054] M_(ij): Mass (kg) of polymers, polymerized in the i^(th) reactorand passed over thereto, out of the polymers in the j^(th) reactor;

[0055] W_(f,i): Mass flow rate (kg/hr) of polymers of inflow to theI^(th) reactor;

[0056] M_(i): Mass (kg) of polymers in the i^(th) reactor;

[0057] W_(f,ij): Mass flow rate (kg/hr) of polymers, polymerized in thei^(th) reactor, out of the polymers fluxed in to the j^(th) reactor;

[0058] W_(o,ij): Mass flow rate (kg/hr) of polymers, polymerized in thei^(th) reactor, out of the polymers discharged from the j^(th) reactor;

[0059] W_(o,i): Mass flow rate (kg/hr) of polymers discharged from thei^(th) reactor;

[0060] W_(i): Polymerization rate (kg/hr) within the i^(th) reactor; and

[0061] T_(i): Temperature (° C.) in the i^(th) reactor.

[0062] Of course, in case of reaction temperature, among two of themathematical formulas of Mathematical Formulas 10˜11 and 12˜13, theforms of Mathematical Formulas 10˜11 should be used to confer somephysical meaning therein. Depending on the characteristics of processvariables, there should be appropriate selections for use amongMathematical Formulas 10˜11 or 12˜13.

[0063] After going through the procedures as above, the instantaneousoperational conditions and cPV's at each stage of the production pointcould be computed.

[0064]FIG. 2 is a graph (case of having residence time distribution ofCSTR), which conceptually explains the method incorporating theresidence time distribution to the respective process variablesaccording to the present invention. In other words, it conceptuallyshows the method of selecting cPV's at some instant while working with asingle reactor with the reactor flow corresponding to a CSTR. Theoperational conditions of a product which is discharged at some instant(t) do not correspond to the operational variables at that instant (t).Rather, they correspond to the values of sum of the values ofoperational variables respectively multiplied by a certain weight factorfrom that instant to some previous point. The sum of the weight factorsis 1, and accordingly the area indicated as “B” is 1. In case of asingle CSTR, the formula of 1−exp[−(t−Δt)/θ] is given. Δt is a timeinterval from t to some previous point in time. θ is the averageresidence time in the reactor. Theoretically, Δt can reach infinity, butit is generally considered up to the time interval of 3˜4 times of θ.

[0065] The operational conditions of a product discharged at an instantt as above do not correspond to the values of operational variables atthat time t. Rather, they correspond to the values of sum of the valuesof operational variables respectively multiplied by a certain weightfactor from that instant to some previous point. The problem caused bythis inconsistency becomes more serious in case of having long residencetime within a reactor, or in case of using a multi-stage reactor. Tosolve this problem, as shown in FIG. 1, it is necessary to employ amethod of setting cPV's in the reactors by stage with respect to thefinal product at some instant in the multi-stage reactor.

[0066] The method of estimating the properties of a polymer product asabove can also be used as a method of monitoring the state of process ofthe polymer product. In other words, in relation to the method ofmonitoring the state of process incorporating the residence timedistribution to the process variables, the method of monitoring hereininvolves theoretically determining the amounts of content and dischargeof the product in the process, and then incorporating the residence timedistribution to said process variables by way of the method of solvingthe balance equations of a hypothetical substance by taking the processvariables as those of the hypothetical substance; and monitoring thestate of process by inputting to various process-state- monitoringmodels cPV's in the reactors by stage with respect to the final productincorporating the residence time distribution to said process variables.

[0067] Moreover, by using the method of estimating the properties of apolymer product as above, it can compute the average operationalconditions appropriate for optimized operation per lot or batch of thepolymer products, and it can also be used in quality control of polymerproducts.

[0068] Moreover, by using the method of estimating the properties of apolymer product as above for the purposes of monitoring the state ofprocesses therein, it can compute the average operational conditionsappropriate for optimized operation per lot or batch of the polymerproducts, and it can also be used in quality control of polymerproducts.

[0069] Below, the present invention as above is described in detail withan example. However, it is for illustrative purposes only and should notbe deemed to limit the present invention in any manner.

[0070] FIGS. 3˜7 are graphs according to one embodiment of the presentinvention. The process therein was a high-density polyethylene reactionprocess in which two reactors were connected serially.

[0071] FIGS. 3˜5 illustrate the changes in raw data (as a function oftime) of various important factors during the operation of ahigh-density polyethylene reaction process. FIG. 3 shows the changes intemperature and pressure within the reactor. FIG. 4 shows the changes inmass flow rates of ethylene and hexane as a function of tine. There,ethylene was the main raw material flowed in to the reactor with adiluent, and hexane was used to control the residence time. Moreover,FIG. 5 respectively illustrates the raw data of mole ratios of hydrogenand ethylene (H₂/C₂) in gas phase within the reactor. There, hydrogenwas used as an agent for controlling the molecular weights of polymers.The mole ratios of hydrogen and ethylene in gas phase were analyzedusing an on-line gas chromatograph. As for the other operationalconditions of the reactor, the capacities of first-stage andsecond-stage reactors were respectively 71 m³, and the production rateof polymers was approximately 20 ton/hr. The reactor residence time forthe first-stage reactor was approximately 2 hours, and approximately 1hour for the second-stage reactor. In particular, FIG. 5 also showscPV's as a function of time, in addition to the raw data of mole ratiosof hydrogen and ethylene (H₂/C₂). As for the computation method ofcPV's, Mathematical Formulas 10˜11 as presented above were used herein.As shown in the figures, in contrast to those of the raw data, thegraphs of cPV's incorporating the residence time distribution of thereactors at each stage showed a form of a very smooth curve. Byinputting cPV's, not the raw data, to the empirical correlation, neuralnetwork, PLS models, etc., the properties of intermediate and finalproducts could be thus obtained.

[0072]FIG. 6 is a graph, which shows the estimated values of melt index(as a function of time) of the intermediate products at the outlet ofthe first-stage reactor during the HDPE reaction process according tothe present invention.

[0073]FIG. 7 is a graph, which shows the estimated values of melt index(as a function of time) of the final products at the outlet of thesecond-stage reactor during the HDPE reaction process according to thepresent invention. For reference, it also shows the estimated values ofproperties (i.e., instantaneous MI) of the case in which the raw datawere directly used instead of cPV's. As shown in the figure, theestimated values of properties (i.e., cumulative MI) based on cPV's havea much better fit against the actual analytical results obtained fromthe laboratory.

[0074] For reference, in the embodiment, the method of empiricalcorrelation was used as a properties estimation model. The method ofempirical correlation in the embodiment is one that expresses melt indexof the polymers in the form of a function of temperature, pressure, andcomposition ratios of the substituents in the process.

[0075] According to the method of estimating the properties of a productby using cPV's in the reactors at each stage with respect to the finalproduct, based on the present invention, it can easily estimate theproperties of a polymer product from a continuous type polymerizationreactor and also monitor the state of each process therein.

[0076] Moreover, according to the present invention, even with a batchor semi-batch type polymerization reactor, or in the reaction system ofuneven treatment of polymers, the method can easily estimate theproperties of the final product while allowing monitoring of the stateof each process therein.

What is claimed is:
 1. A method of estimating the properties of apolymer product, which comprises the steps of: computing convertedprocess variables (cPV's) which means process variable that final orintermediate product experienced earlier in average in the reactors bystage with respect to the final product by incorporating the residencetime distribution to process variables by means of theoreticallydetermining the amounts of content and discharge of the product in theprocess, and then solving the balance equations of a hypotheticalsubstance by taking the respective process variables as those of thehypothetical substance; and estimating the properties of the product byinputting to various property estimation models cPV's in the reactors bystage with respect to the final product after incorporating theresidence time distribution to said process variables.
 2. The method ofestimating the properties of a polymer product according to claim 1,wherein said process is a process which uses a single polymer reactor ora multi-stage polymer reactor.
 3. A method of monitoring the state ofprocess, incorporating the residence time distribution to processvariables, wherein said method comprises theoretically determining theamounts of content and discharge of the product in the process, and thenincorporating the residence time distribution to said process variablesby way of the method of solving the balance equations of thehypothetical substance by taking the respective process variables asthose of the hypothetical substance; and monitoring the state of processtherein by inputting to various process-state-monitoring models cPV's inthe reactors by stage with respect to the final product afterincorporating the residence time distribution to said process variables.4. The method of monitoring the state of process according to claim 3,wherein said process is a process which uses a single polymer reactor ora multi-stage polymer reactor.
 5. A method of controlling the propertiesof a product, which comprises computing the average operationalconditions appropriate for optimum operation of the polymer product perlot or batch by using the method of estimating the properties of apolymer product according to claim 1; and then utilizing the same inquality control of the polymer product.
 6. A method of controlling theproperties of a product, which comprises computing the averageoperational conditions appropriate for optimum operation of the polymerproduct per lot or batch by using the method of monitoring the state ofprocess according to claim 3; and then utilizing the same in qualitycontrol of the polymer product.
 7. The method of controlling theproperties of a product according to claim 5 or 6, wherein said processis a process which uses a single polymer reactor or a multi-stagepolymer reactor.
 8. The method of monitoring the state of processaccording to claim 3 or 4, wherein said process is a general chemicalprocess.
 9. The method of controlling the properties of a productaccording to claim 5 or 6, wherein said process is a general chemicalprocess.